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Invariant Integrals for the Equilibrium Problem for a Plate with a Crack

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Abstract

We consider the equilibrium problem for a plate with a crack. The equilibrium of a plate is described by the biharmonic equation. Stress free boundary conditions are given on the crack faces. We introduce a perturbation of the domain in order to obtain an invariant Cherepanov–Rice-type integral which gives the energy release rate upon the quasistatic growth of a crack. We obtain a formula for the derivative of the energy functional with respect to the perturbation parameter which is useful in forecasting the development of a crack (for example, in study of local stability of a crack). The derivative of the energy functional is representable as an invariant integral along a sufficiently smooth closed contour. We construct some invariant integrals for the particular perturbations of a domain: translation of the whole cut and local translation along the cut.

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Authors
  1. E. M. Rudoy
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Rudoy, E.M. Invariant Integrals for the Equilibrium Problem for a Plate with a Crack. Siberian Mathematical Journal 45, 388–397 (2004). https://doi.org/10.1023/B:SIMJ.0000021293.61120.35

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  • DOI: https://doi.org/10.1023/B:SIMJ.0000021293.61120.35

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